Recently, J. Carrasquel, studied in [1]} rational approximations of sectional category of any continuous map \(f : X\rightarrow Y\)  between finite type simply connected spaces ([2]}, §1 for definition). He especially uses the characterisation Ã  la FÃ©lix-Halperin to give explicit definitions of \(TC_n(X_0)\)  (resp. \(mTC_n(X)\) , \(HTC_n(X)\) ), higher (resp. module, homology) topological complexity of \(X_0\)  (\(n\ge 2\) ). These homotopy invariants are indeed similar to \(cat_{LS}(X_0)\) , \(mcat_{LS}(X)\)  (the module LS-category) and \(e_{\mathbb {K}}(X)\)  respectively. He also remarked that since \(\Delta ^n_{X_0}=(\Delta ^n_X)_0\) , the rationalization of the \(n\)  diagonal map \(\Delta ^n_X\) , then
\(nil \ker H^*(\Delta ^n_{X})=\sup \lbrace m\; |\; (\ker H^*(\Delta ^n_{X}))^m\ne 0\rbrace \) 
